1. Field of the Invention
The invention relates to phasing the segmented aperture of a telescope to ensure good image quality. In particular we give a simple, image-based method to detect and correct piston errors which are integer multiples of the central wavelength λ.
2. Description of Prior Art
A segmented aperture has mirror segments which are phased separately to combat instabilities associated with the size of the mirror. A typical system is the Keck telescope in Hawaii which has 36 segments in each of two telescopes [2] and another is the James Webb Space Telescope (JWST), currently under development, which has 18 segments [3]. Good image quality is achieved when the segments are perfectly phased, that is, when the segments are positioned to mimic an ideally shaped, single mirror.
Telescopes with a segmented aperture use a plurality of methods to align the segments. See U.S. Pat. Nos. 3,842,509, 4,946,280, 5,109,349, 5,113,064, 5,128,530, 6,649,895, and 7,372,569; and References [2-9]. The most common method is a dispersed Hartmann sensor, which measures light from a point source as seen through multiple apertures positioned to overlap adjacent segments. Two examples of this method are in U.S. Pat. No. 6,649,895, entitled, “Dispersed Hartmann sensor and method for segment alignment and phasing,” and in U.S. Pat. No. 7,372,569, entitled, “Method of correcting alignment errors in a segmented reflective surface.” The former uses a Hartmann lenslet and a dispersive element to measure the size of discontinuities in the wavefront; and the latter has sub-apertures across the abutting edges of reflective segments and sensors for each of the sub-apertures.
The present invention is much simpler than a dispersed Hartman sensor. It uses image-based wavefront sensing, whereby images measured in the focal plane of a telescope are processed by computer to estimate the phase in the aperture of the telescope. The first such image-based wavefront sensor was disclosed in U.S. Pat. No. 4,309,602 by Gonsalves, et al. and modifications are in U.S. Pat. Nos. 5,384,455 and 6,107,617. References [2] through [19] describe additional background on image-based wavefront sensing. The method was used in 1990 to estimate the flaw in the Hubble Space Telescope [19].
The James Webb Space Telescope will use dispersed Hartmann sensing for coarse phasing of its 18 segments and monochromatic, image-based wavefront sensing for fine phasing [3,9]. The latter method will also use phase diversity, a method disclosed in U.S. Pat. No. 4,309,602 and described fully in Reference [14].
A segmented aperture presents an interesting challenge for such a monochromatic, image-based wavefront sensor. The method is subject to “piston ambiguity” [1], wherein segments can be displaced by a non-zero multiple of λ, the wavelength of the measured data, but the displacements are unobservable at that wavelength. When a segment is so displaced we say that it has a “piston wrap.”
In Reference [1] Löfdhal and Ericksson discuss piston ambiguity in the context of phasing the Keck II telescope. They study the well-known benefit of wideband measurements to reduce piston ambiguity and suggest appropriate wavelengths at which to make measurements based on the theory of continued fractions.
In contrast to Reference (1) which provides no process, machine or article of manufacture to reduce the authors' theory to practice, the present invention is a new, unobvious, and useful method to measure and to correct piston ambiguities. The present invention uses focal plane measurements at one wavelength λ to make an initial alignment of the segments. Then it uses focal plane measurements at a new wavelength λ1 to form a unique image of the piston wraps. The method is simple and direct.
The prior art for this invention includes image-based wavefront sensing in the form of phase-diverse phase retrieval. This prior art includes U.S. Pat. Nos. 4,309,602, 5,384,455, and 6,107,617; and References [2-4, 9-17]. This is a mature technology with two basic approaches: (1) the iterative transform algorithm (ITA), in which the wavefront (phase in the aperture ) is estimated, iteratively, by imposing physical constraints in spatial and in spatial frequency domains; and (2) model-based phase retrieval (MBPR) in which a weighted sum of basis functions is manipulated so that a model for the data fits the observed data. The observed data is often an image in best focus and one or more images out of focus.
The continuity of phase across each segment of the aperture ensures that phase-retrieval-based algorithms will give high-quality estimates across each segment. But potential discontinuities between segments allow the piston estimates to have piston wraps. These wraps are not detectable at the measurement wavelength λ. The telescope might have perfect imaging at wavelength λ but the telescope could have degraded imaging at other wavelengths. This will cause distortion in wideband (multi-colored) images which fall on a broadband detector.